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Archived Comments for: Properties of right fractional sum and right fractional difference operators and application

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  1.  A comment on the article "Properties of right fractional sum and right fractional difference operators and application

    Thabet Abdeljawad, No competing intersets exist.

    3 February 2016

    Advances in Difference Equations (2015) 2015:288"

    Competing interests

    Recently, the authors in the article [h] "Zuoshi Xie and Chengmin Hou, Properties of right fractional sum and right fractional difference operators and application, Advances in Difference Equations (2015) 2015:288" claimed that they introduced the right fractional sum and the right fractional difference for the first time and they gave the proof of their properties. In fact they defined the right fractional sum and difference operator in the delta sense and denoted by "$~_{b}\nabla^{-\nu}$" and "$~_{b}\nabla^{\nu}$", respectively. The authors in [a] introduced exactly the same in early 2011 and denoted by "$\nabla^{-\alpha}_b$" and "$\nabla^{\alpha}_b$", respectively. Then, the author in [b]continued the study of these operators. It is obvious that most of the results given in [h] are repetition to what was done in \cite{a} and \cite{b} and no citation was given to them. Moreover, T. Abdeljawad in [d]and \cite{e} studied right and left delta and nabla fractional sums and differences within dual identities ($\Delta_a^{-\alpha}, ~_{b}\Delta^{-\alpha}, \nabla_a^{-\alpha}, ~_{b}\nabla^{-\alpha})$ and $\Delta_a^\alpha, ~_{b}\Delta^\alpha, \nabla_a^\alpha, ~_{b}\nabla^\alpha$) and he related the left and right ones  by the $Q-$ operator to confirm his definitions. Furthermore, right  delta and nabla fractional sums have been studied more extensively, in [c], [f] and [g]. Finally, it is noted  that none of the references [a]-[g] have been cited in [h].








    Refrences:


    [a]Thabet Abdeljawad,and Dumitru Baleanu, Fractional Differences and Integration by Parts, Journal of Computational Analysis nad Applications ,vol 13 no. 3 , 574-582 (2011).


    [b]  Thabet Abdeljawad, On Riemann and Caputo Fractional Differences, Computer and Mathematics with Applications, vol. 62 (3), 1602-1611 (2011).


    [c] Thabet Abdeljawad, F. Atici, On the definitions of nabla fractional differences, Abstract and Applied Analysis, Volume 2012 (2012), Article ID 406757, 13 pagesdoi:10.1155/2012/406757.


    [d] Thabet Abdeljawad, Dual identities in fractional difference calculus within Riemann, Advances in Difference Equations, 2013, 2013:36.


    [e] Thabet Abdeljawad,  On Delta and Nabla Caputo Fractional Differences and Dual Identities, Discrete Dynamics in Nature and Society, Volume 2013 (2013), Article ID 406910, 12 pages.


    [f] Thabet Abdeljawad, Nabla Euler-Lagrange Equations in Discrete Fractional Variational Calculus within Riemann and Caputo, Int. J. of Mathematocs and Computation, Vol. 22 (1) , 144-15(2014).

    [g]Thabet Abdeljawad, Dumitru Baleanu, Fahd Jarad, Ravi Agarwal, Fractional sums and difference with binomial coefficients, Discrete Dynamic Systems in Nature and Society, Volume 2013 (2013), Article ID 104173, 6 pages.

    [h] Zuoshi Xie and Chengmin Hou, Properties of right fractional sum and right fractional difference operators and application, Advances in Difference Equations (2015) 2015:288.




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